What are the difference between center and centre?

The difference lies between American nomenclature and the Queen's English nomenclature. The Queen's English may not speak only for Britain, but also former Queen colonies as well, this prevails strongly in Canada. Many ways to spell words have evolved over the past decades just as chinese have through different dynasties.

Examples are as follows: (American v. Queen's English)
Center v. Centre
Labor v. Labour
Color v. Colour

Other than that, the meaning of the word is exactly the same, as they are all derived from the same family - Anglo Group.

同一意思﹐都係解作“中心”﹐只是串法不同而已！

center﹙美式﹚
centre﹙英式﹚

center- 美式英語 centre - 英式英語. All the same.

Actually, there is no any difference between them, you can use either when you are being in need
e.g. " Where are you now?", " I'm outside the entrance of plaza near the town centre (or center)."
e.g. The center (or centre) of estate.

center maybe the meaning is different of centre
Centre
Center

er & re is different